## Algebra and Trigonometry 10th Edition

$x= -1; y= 2; z= 0$
A system of equations can be written in the form: $AX=B$ where $B= \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ When there exists an inverse of a matrix, the following relationship is true: $A A^{-1} = I$ Thus, $X=A^{-1} B = \begin{bmatrix} 2& 3 & 5 \\ 3 & 5 & 9 \\ 5 & 9 & 17 \end{bmatrix} \begin{bmatrix} 4 \\ 7 \\ 13 \end{bmatrix}$ Now, we will use the Row Reduced Echelon Form. $X= \begin{bmatrix} 1 & 0 & -2 & : & -1 \\ 0 & 1 & 3 & : & 2 \\0 & 0 & 0 & : & 0 \end{bmatrix}$ Therefore, $x= -1; y= 2; z= 0$